On the strong product of a k-extendable and an l-extendable graph

Let G(1) circle times G(2) be the strong product of a k-extendable graph G(1) and an l-extendable graph G(2), and X an arbitrary set of vertices of G(1) circle times G(2) with cardinality 2[(k + 1) (l + 1)/2]. We show that G(1) circle times G(2) - X contains a perfect matching. It implies that G(1) circle times G(2) is [(k + 1)(l + 1) /2]-extendable, whereas the Cartesian product of G(1) and G(2) is only (k + l + 1)-extendable. As in the case of the Cartesian product, the proof is based on a lemma on the product of a k-extendable graph G and K-2. We prove that G circle times K-2 is (k + 1)extendable, and, a bit surprisingly, it even remains (k + 1)-extendable if we add edges to it.